While the hypothesis that the Higgs boson at 125 GeV is a pure \({\cal CP}\) -odd state was ruled out based on LHC Run 1 data [1]}, [2]}, only rather weak bounds exist on a possible admixture between a \({\cal CP}\) -even and a \({\cal CP}\) -odd component. The analyses so far were mainly based on observables involving the coupling of the observed Higgs boson, \(H\) , to two gauge bosons, \(HVV\) , where \(V = W, Z\) , in particular \(H \rightarrow ZZ^* \rightarrow 4 \ell \) , \(H \rightarrow WW^* \rightarrow \ell \nu \ell \nu \) , and Higgs production in weak vector boson fusion (VBF). Since in many BSM models only a small loop-induced coupling of a \({\cal CP}\) -odd component to gauge bosons, \(H^{{\cal CP}-{\rm odd}}VV\) , is generated, the effects of the \({\cal CP}\) -odd component are heavily suppressed compared to the tree-level contribution of \(H^{{\cal CP}-{\rm even}}VV\) , even if the \({\cal CP}\) -odd component itself is large. Consequently, the couplings of the observed Higgs boson to fermions (in particular to the top quark) are crucial for investigating the \({\cal CP}\) -nature of the observed state, since a \({\cal CP}\) -odd component in the \(Hf \bar{f}\)  coupling may be unsuppressed and could be of similar magnitude as the \({\cal CP}\) -even component. In addition to being a spectacular discovery by itself, the establishment of a non-zero \({\cal CP}\) -odd component of the top-Yukawa coupling would also be a strong hint for an extended BSM Higgs sector.
